In new tests comparing the educational performance of 15-year-olds worldwide, United States teenagers performed about average in reading and science, but below average in mathematics, a trend that has shown no major changes since the testing began in 2000.

Yet while US students were treading water since the tests were last given, their peers in several other countries surged past them, according to the Program for International Student Assessment, or PISA, conducted every three years. The 2012 results were released Tuesday.

Education Secretary Arne Duncan said the US results painted “a picture of educational stagnation,” while a range of critics decried the failure of US education policies.

More than 510,000 15-year-old students in 65 countries and other education programs took part in the 2012 PISA test. Students from Shanghai-China, Hong Kong, Singapore, Japan, and South Korea scored highest in all three subjects. Switzerland and the Netherlands also ranked near the top.

Set against that backdrop, the US performance in mathematics drew the most handwringing by far. Among 65 nations and jurisdictions where the PISA test was administered, 29 countries and provinces outperformed the US in math in 2012, compared with 23 in 2009, the last time the test was given.

The list of those racing past the US included not only perennially strong competitors like Singapore and South Korea , but also Latvia, Australia, and Vietnam when compared with test results from three years earlier.

In reading, US scores were flat. But students in 19 countries scored higher than the US in 2012, compared with just nine countries three years before. Steady gains by Poland and Germany leapfrogged them past the US along with Estonia, Ireland, and Chinese Taipei (Taiwan).

In science, meanwhile, some 22 countries’ educational systems beat out the US average, compared with 18 in 2009.

Overall, the US had a “flat line” performance as other nations surged, said Secretary Duncan. “While we are seeing some encouraging progress on many important measures, the United States’ performance on the 2012 PISA is a picture of educational stagnation,” he said in a statement. “This is a reality at odds with our aspiration to have the best-educated, most competitive workforce in the world.”

Even though the US spends more on education than all but a handful of countries, that spending has not translated into better-prepared students, according to the new PISA test, which is coordinated by the Paris-based Organization for Economic Cooperation and Development, or OECD.

At the same time, static US performance and surging competitors have given fresh ammunition to education critics across the spectrum ­– from those who oppose standardized testing to those unhappy with the new Common Core approach to setting national standards – and others taking aim at US mathematics education.

“The current ‘education reform agenda’ is bankrupt,” said Marc Tucker, president of the National Center on Education and the Economy, an education advocacy organization. “There is no evidence that it can succeed. It is time to embrace a very different education reform agenda, the one that has proven itself in the PISA rankings.”

Teachers’ representatives, meanwhile, interpreted the results to mean that current state and federal policies have fallen short of helping teachers.

“Sadly, our nation has ignored the lessons from the high-performing nations,” American Federation of Teachers President Randi Weingarten said in a statement. “These countries deeply respect public education, work to ensure that teachers are well-prepared and well-supported, and provide students not just with standards but with tools to meet them – such as ensuring a robust curriculum, addressing equity issues so children with the most needs get the most resources, and increasing parental involvement.”

She included a pot-shot at state standardized test results used to evaluate teachers and school performance.

“None of the top-tier countries, nor any of those that have made great leaps in student performance, like Poland and Germany, has a fixation on testing like the United States does,” Ms. Weingarten noted.

It’s not that US policymakers have been idle, of course. In 2010, President Obama launched “Race to the Top,” an ambitious policy shift aimed at encouraging US states to adopt international benchmarks as a framework for preparing student for college. It also ramped up efforts to recruit and reward effective teachers, measure student success, and inform teachers and principals how to boost performance.

A separate state-led effort to establish a single set of clear voluntary standards for K-12 in English and mathematics also has been launched. The new Common Core academic standards in math and reading that have been adopted by 45 states and the District of Columbia could help raise the nation’s PISA scores, according to a report by the OECD, which set up the test in 2000 as a way to compare public education systems worldwide.

Yet achievement gaps remain along ethnic and socioeconomic lines despite US education spending that is near the top worldwide on a per student basis.

“Our students from well-to-do families have consistently done well on the PISA assessments,” Dennis Van Roekel, president of the National Education Association, said in a statement. “For students who live in poverty, however, it’s a different story. Socioeconomic factors influence students’ performance in the United States more than they do in all but a few of the other PISA countries.”

Still, Jack Buckley, commissioner of the National Center on Education Statistics, which oversees the US PISA exams, cautioned that the test could measure performance – but not the reasons for that performance.

Some critics regularly dismiss low US scores on PISA, citing the major socioeconomic challenges faced by the US, compared, for instance with Shanghai, a haven for China’s elite that topped PISA’s charts in all categories.

But the report identifies some countries where educational achievement is not so closely tied to wealth and other factors, including Estonia and Japan.

The PISA data also show five countries with a higher proportion of immigrants in their student population, and some of these outperform the US, notes the National Center on Education and the Economy.

“Many allege that one cannot compare the US with other countries because the US is far more diverse than they are,” said Mr. Tucker. “But the PISA data show that the share of students in US schools who are disadvantaged is about average for the countries in the survey.”

One bright spot was in the results for students in three US states – Massachusetts, Connecticut and Florida. While Florida’s score was on par with the US average, Massachusetts, long at or near the top of US educational performance, outperformed all but three education systems, with Connecticut close behind.

"The performance of our 15-year-olds, particularly in reading where they scored among the world's leaders, reflects the tremendous efforts of educators and students statewide to achieve a world-class education," Massachusetts Commissioner of Elementary and Secondary Education Mitchell Chester said in a statement. "The top performing countries are actively working on upgrading their program of study, and so is Massachusetts.”

[Editor's Note: The original version of this story misidentified Randi Weingarten as a "Mr.," rather than "Ms."]